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F
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SU(3)SU(2)U(1)
ii Fi
i, i, Fi , = 1, 2
i = i,i = i()i + Fi,
Fi = i() (i),
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gaugeAa = a + gfabcAbc
gaugea = gfabcbc,
gaugeDa =
a + gfabcAbc
fabcTa, Tb
= ifabcTc
Lgauge = 14
FaFa + iaD
a +1
2DaDa
Fa
Fa = Aa Aa + gfabcAbAc,
Da = a + gfabcAb
c.
gaugeXi = iga((Ta)jiXj)
DXi = Xi
igAa(T
a)jiXj
Xi
i, i, Fi
igAa(Ta)jiXj
a Da
(iTaji j)a, h.c. (iTaji j)D
a
S = 0
i = i,
i =
i()D
i + Fi,
Fi = i() (Di) + 2g(Taij j)a
L = Lchiral + Lgauge
2g(iTaji j)a + h.c. + g(iTaji j)D
a
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Lchiral = DiDi + iiDi + FiFi+(1
2
2W
ijij +
W
iFi) + h.c.
V
V = FiFi +1
2
a
DaDa
=
i
W
i
W
i
+
1
2
a
g2a(iT
aji j)
2
W
i = Mij
j +
1
2y
ijk
jk.
12
yijkijk + h.c.
+1
4
yijnyklnijkl
3
1
2Minyjkni
jk + h.c.
MikMkjij
1
2 Mij
ij + h.c.
14
FaFa
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DiDi + iiDi + iaDa
Da = a + gfabcAb
c.
Di = i igAa(Ta)jijDi = i igAa(Ta)jij
2g(iTaji j)a + h.c
g2a(iT
aji j)
2
Q |fermion = |boson , Q |boson = |fermion ,
Q, Q
= 2()P
{Q, Q} = 0 =
Q, Q
[Q, P] = 0 =
Q
, P
m2b |boson = P2 |boson = QP2 |fermion = m2f |boson m2b = m2f
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0P0 0 = 1
4
0Q1, Q1 + Q2Q2 0
=1
4
Q1 |02 + ||Q1 |0||2 + Q2 |02 + Q2 |02
Q Q |0 = 0Q |0 = 0
Lsoft
L = LSuSy + Lsoft
dx4Lsoft = 0
Lsoft
Lsoft = 1
2Ma
aa +1
6aijkijk +
1
2bijij + h.c. (m
2)ijji
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Qa
(x) (x) = (x) + ia[(Qa), (x)],
d4x
L[]
(x)(Qa)(x) = 0 and | (x) | = 0,
Qa | =0
[Q, (x)] = i(x), | (x) | = 0,
(x) (x)| (x) | = | [Q, (x)] | = 0
Q | = 0
(x)
Qa |0 = 0 0 P0 0 > 0
0P0 0 = 0 |V| 0
V = FiFi +1
2
k
DakDak
k
F D
0 |F| 0 = 0, or 0 |Da| 0 = 0,
Fi = 0 and Da = 0
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U(1)D
LFI = D, [] = M2D = (...) D
V|D = D 12
D2 gDi
qi |i|2 , D = gi
qi |i|2 ,
V =i
|mi|2 |i|2 + 12
g
i
qi |i|22
.
V > 0Qa |0 = 0|mi|2 gqi |mi|2
F
Fi
i, i, F
i
i = 1,...,nW Fi = (Wi ) = 0 i
V =
i |Fi|2 > 0Qa |0 = 0
i, i, F
i
i = 1, ..., 3
W
W = k1 + m23 + g2
12
3, k, m,g > 0,
1
V =
k g2
|3|22
+ m2 |3|2 + |m2 + g13|2 > 0,
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m2 > gk
3
= 0 = 2
1
1V =
i |Fi|2
F1 = ki = 0
V = V(0) + mijij + O(3),
mij =2V
ij|0 = mji
0, 0, m2, m2, m2 gk, m2 + gk, 1
2
2W
i
j
ij
0, m2, m2, 1{1, 1, F1}
Q
F
LsoftF
LsoftF
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hmc
2Gmc2
F
LNR = 1Mp
F1
2da
aa +1
6y
ijkijk +1
2
ijij+h.c. 1
M2pF Fkiji
j
F 0 |F| 0 = 0 Lsoft
Lsoft = 12
Maaa 1
6aijkijk 1
2bijij (m)2ij ji
Ma =0|F|0Mp
da
F
